When learning a new skill, it’s best to master a single, simple approach before being exposed to other more complex methods. Otherwise, you run the risk of confusion, frustration and ultimately not learning how to solve the problem.

Take directions.

If you’re lost and you ask for directions, you don’t want someone to tell you five ways to reach your destination. You want one, relatively simple way to get there – preferably with the least amount of turns and the highest number of landmarks.

Maybe later if you’re going to be traveling to this place frequently, you may want to learn alternate routes. But the first time, you’re more concerned about finding the destination (i.e. getting the answer) than understanding how the landscape would appear on a map.

This is the problem with Common Core math. It doesn’t merely ALLOW students to pursue alternate methods of solving problems. It REQUIRES them to know all the ways the problem can be solved and to be able to explain each method. Otherwise, it presumes to evaluate the student’s understanding as insufficient.

It introduced set theory, forcing students to think of numbers as groups of objects rather than abstractions to be manipulated. In an advanced undergraduate mathematics course, this makes perfect sense. In first grade, it muddles the learning tremendously.

To make matters even more perplexing, it mandates students look at numbers with bases other than 10. This is incredibly confounding for elementary students who often resort to their fingers to help them understand early math.

Tom Lehrer wrote a very funny song about the new math which shows how confusing it can be. The methods used to solve the problem can be helpful but an emphasis on the conceptual underpinning at early ages perplexes more than it helps:

Popular culture is full of sly references to this old New Math. Charles Schultz wrote about it in several Peanuts comic strips in 1965. In one such strip, kindergartener Sally gets so frustrated trying to solve a New Math problem she cries, “All I want to know is, how much is two and two?” New Math even made an appearance in the 1973 movie “There’s No Time for Love, Charlie Brown,” in which the titular Brown asks “How do you do New Math problems with an old Math mind?”

In the 1992 episode of the Simpsons, “Dog of Death,” Principal Skinner is elated that an influx of school funding will allow him to purchase school improvements. In particular he wants to buy history books that reveal how the Korean War ended and “math books that don’t have that base six crap in them!”

So where did this idea for New Math come from?

In 1957, the Soviets launched Sputnik sending Americans into a panic that they were being left behind by these Communist supermen. As a result in 1958, President Dwight D. Eisenhower passed the National Defense Education Act which dramatically increased school budgets and sent academics racing for ways to reform old practices. One product of this burst of activity was the New Math.
A decade later, it was mostly gone from our public schools. Parents complained they couldn’t help their children with homework. Teachers complained they didn’t understand it and that it needlessly confused their students.

Fast forward to 1983 and President Ronald Reagan’s National Commission on Excellence in Education. The organization released a report called “A Nation at Risk” that purported to show that public schools were failing. As a result, numerous reforms were recommended such as increased standardization, privatization and competition.

It is hard to overemphasize how influential this report was in education circles. Even today after its claims have systematically and thoroughly been debunked by statisticians like those at Sandia National Laboratories, politicians, pundits and the media persist with this myth of failing public schools.

“A Nation at Risk” birthed our modern era of high stakes testing and, in 2009, Common Core.

In some ways, the Core is worse than the old New Math because of its close connection with high stakes testing. In the ‘60s if a child didn’t understand how to add, he failed math. Today, if a child does that, he fails the standardized test and if that happens to enough students, his school loses funding, his teacher may be fired and his school may be closed. As such, the pressure today’s children undergo is tremendous. They aren’t just responsible for their own learning. They’re responsible for the entire school community.

21 thoughts on “Common Core’s New New Math has the Same Problem as the Old New Math”

What is the difference between Pre-Algebra, now called “Accerated Math” and “Integrated Math”. Here in CA they don’t call Pre-Algebra, Pre-Algebra and they don’t call Algebra 1, Algebra 1. Instead they now call it “Accerated Math”/”Integrated Math”. Any thoughts why the common core wouldn’t stick to Algebra instead of “integrating and accerating it” with geometry, statistics, probability, and anything else they think to throw into the mix. What’s up with that?

Utah went to an entirely integrated math. I’m not a math teacher, but my understand is that they threw all of the math disciplines into the air, and then grouped them by where they landed. As a result, the math is HUGELY developmentally inappropriate. My son, who struggled with math anyway, got stuck in Secondary I in 9th grade, that required him to do calculus. I know this because his high schooler tutor said that she was doing the same thing, at the same time, in AP Calculus.

Not to mention that the math jumps like crazy from one concept to another, without any coherency at all. The math teachers at my school can’t even explain why one concept follows another. Add into that throwing kids into the middle of the curriculum (instead of starting in Grade 1 and building up from there), and the math here is a DISASTER. The districts are saying that they are getting HUGE numbers of kids that are suddenly qualifying for special education services in middle school. At my school of 900 middle school students, we had 75 NEW referrals for special education last year, and about 60 of those qualified. These are kids who didn’t qualify earlier in elementary school. Why have a core that is creating “deficiencies” in kids?

And Utah’s math core was considered an “A” core but the Fordham foundation, but went to this mess. Makes no sense.

As it happens i have three kids. The oldest has a math brain. He went through everyday math, learned all the oddball ways of computing, chose the best method and reaped huge rewards. He graduated based on his SAT scores. (In NJ you must pass the SAT or the PARCC to graduate) Everyday math gave him an intrinsic understanding that took a good math student and made him great.
My second son is a lazy unmotivate student with moderate math ability. He, to, did everyday math, chose his prefered method , and failed the PARCC. Why? He got the correct answer, but lost points because he did not use the PARCC approved method for solvimg the problem.
My third son has dyslexia and dyscalcula. He will never pass the tests.
I am pleased that the “new” math was able to sharpen an already good math brain, but my average and my special ed kids have been harmed. There has got to be a better way.

Sue–If I may suggest–your second son is NOT lazy and unmotivated. To gain a better insight into all your children, I highly recommend that you read The End of Average by Todd Rose. Your perception of your son is blinding you to his strengths. Is being GREAT at math really “smarter” than being great at art, or music, or game design, or coding, or whatever it is that he really ENJOYS doing and is good at? The better way that you are looking for is learner-centered education that sees, hears, understands, and respects each child as an individual rather than trying to clone them into some one-size-fits-all standard. The only purpose that serves is making sure that there are “failures” and “losers” who will do the service jobs that we can’t function without instead of helping them “succeed” in their own terms.

TEACHING all the ways to solve a problem IS the problem. In learner-centered schools, learners are given a problem and a suggestion of one way it might be solved. But they are also free to figure out their own ways to solve it. They aren’t REQUIRED to learn all the ways. They are simply ENCOURAGED to figure out other ways you might solve the same problem. One example: In one learner-centered school, learners were challenged to come up with as many ways as possible to build 42. Then they produced a visual depiction of their responses. It was a challenge–not a teacher-directed lesson. You can find the result on page 16 of this article. http://teachinginmind.com/pdf/renaissance-school-of-arts-and-sciences.pdf

The idea that all children have to “know and be able to do” the same things at the same age and in the same way is the elephant in the room. Why? Do all “successful” adults know the same things? Can they all DO the same things? Is it even developmentally possible? NO! It’s just an easy way for test publishers to be able to write multiple choice questions that do NOT measure learning.

If people are interested in what mathematicians think about what is taught as mathematics in K-12 (and the first couple of years of college), A Mathematician’s Lament by Paul Lockhart is a good place to start (https://www.maa.org/external_archive/devlin/LockhartsLament.pdf). In his view the old way of teaching math is like using paint by numbers sets to teach art.

Sure children could be allowed to paint a rainbow in many different ways, and “it sounds fine in theory – until you think about it for five minutes.

When learning a new skill, it’s best to master a single, simple approach before being exposed to other more complex methods. Otherwise, you run the risk of confusion, frustration and ultimately not learning how to solve the problem.”

That is why all painting should be done using paint by numbers sets. Students can only handle the complexity inherent in facing a blank piece of paper after they have mastered painting by numbers.

Teaching economist, you espouse exactly the kind of hubris that got us into this mess. You teach at the college level. You know the subject matter backwards and forwards. However, you have no training in child development, no experience with how children learn. It would make the most sense to listen to people with training and experience in this field, but no. You know everything. This is why Common Core fails – no respect for working K-12 educators.

Also, you may find this article interesting; it uses the same metaphor you use in your article:

“An example of this is the plight of a visitor to a new city trying to find his way around. In getting from Point A to Point B, the visitor may be given instruction that consists of taking main roads; the route is simple enough so that he is not overburdened by complex instructions. In fact, well-meaning advice on shortcuts and alternative back roads may cause confusion and is often resisted by the visitor, who when unsure of himself insists on the “tried and true” method. The visitor views these main routes as magic corridors that get him from Point A to B easily. He may have no idea how they connect with other streets, what direction they’re going, or other attributes. With time, after using these magic corridors, the visitor begins see the big picture and notices how various streets intersect with the road he has been taking. He may now even be aware of how the roads curve and change direction, when at first he thought of them as more or less straight. The increased comfort and familiarity the visitor now has brings with it an increased receptivity to learning about – and trying – alternative routes and shortcuts. In some instances he may even have gained enough confidence to discover some paths on his own.”

The problem with both “paint by numbers” and the “directions” analogy is that not all people think alike. The “simplest” directions for one person may be less than simple for someone who prefers directions that include north, south, east west, or street names/route numbers combined with the number of miles or blocks, the number of stoplights before a turn, or landmarks (turn left at Walmart). ALL of these preferences exist…and more! Just think about how people have given you directions when you asked–and which ones made more sense to you.

I agree that offering a few possibilities for tackling a math problem may make it much easier, but the issue is that “teaching” what one perceives to be the “simplest” way to solve a problem (the way in the textbook) is often accompanied by test questions that require that way in order to solve them. So rather than encouraging learners to notice other ways to solve the problem and choose the one that makes the most sense to them, we often discourage that so that they will score well on the test!

Does “paint by numbers” really help a person learn to paint? Or just to follow directions? Metaphors like this are extremely useful, but no metaphor has a complete one-to-one correspondence to the situation to which one is comparing it. Becoming proficient in math is based on understanding ways in which operations are related to one another (e.g. multiplication is repeated addition). I sometimes wonder if math teachers realize that the way they choose to solve a problem is one of many valid solutions that may seem as obvious to other people as their way does to them.

What is called math education today is primarily an education in following directions. At one time I thought that there was simply more variation in student’s mathematical abilities than student abilities in subject like language arts. I have come to realize that the way we teach mathematics so confines student’s talents and creativity that even slight differences in a students mathematical abilities results in large differences in where they should be placed in the standard mathematics curriculum, something not necessary in courses in the language arts.

A writing assignment in a language arts class gives the student the possibility of writing a poem or short story that could be published in the New Yorker or an essay that would appear in The Journal of Modern Literature. There is no assignment in a K-12 math class that allows for the possibility of professional quality work from a student. and if the student turned an assignment into one that allowed him or her to do professional quality work, the student would fail the assignment.

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As a middle school math teacher with over 30 years in the class room, I couldn’t agree more. Kids need a quick efficient way to add, subtract, multiply and divide. I do think they need time to “play” with numbers and discover relationships and patterns, but not at the expense of fluency.